PHP ,72 Bytes

do$r=OAEIHBKD[$t*4+($n=&$argv[1])%4].$r;while(($t=!$t)|$n=$n>>2);echo$r;

76 Bytes alternative Version

for($i=2*strlen(dechex($n=$argv[1]));$i;)echo HBKDOAEI[$i%2*4+$n/4**--$i%4];

PHP ,63 Bytes

contribution by @Titus Thank You

for($n=$argv[1];$n;$n>>=4)$r=HBKD[$n/4&3].OAEI[$n&3].$r;echo$r;

72 Bytes works also with zero

do$r=OAEIHBKD[$t*4+($n=&$argv[1])%4].$r;while(($t=!$t)|$n=$n>>2);echo$r;

76 Bytes alternative Version

for($i=2*strlen(dechex($n=$argv[1]));$i;)echo HBKDOAEI[$i%2*4+$n/4**--$i%4];

PHP ,74 Bytes

do{$r=OAEIHBKD[$t*4+($n=&$argv[1])%4].$r;}while(($t=!$t)|$n=$n>>2);echo$r;

76 Bytes alternative Version

for($i=2*strlen(dechex($n=$argv[1]));$i;)echo HBKDOAEI[$i%2*4+$n/4**--$i%4];

PHP ,72 Bytes

do$r=OAEIHBKD[$t*4+($n=&$argv[1])%4].$r;while(($t=!$t)|$n=$n>>2);echo$r;

76 Bytes alternative Version

for($i=2*strlen(dechex($n=$argv[1]));$i;)echo HBKDOAEI[$i%2*4+$n/4**--$i%4];

PHP ,80 Bytes

$c=OAEIHBKD;do{$r=$c[$t*4+($n=&$argv[1])%4].$r;}while(($t=!$t)|$n=$n>>2);echo$r;

PHP ,74 Bytes

do{$r=OAEIHBKD[$t*4+($n=&$argv[1])%4].$r;}while(($t=!$t)|$n=$n>>2);echo$r;

76 Bytes alternative Version

for($i=2*strlen(dechex($n=$argv[1]));$i;)echo HBKDOAEI[$i%2*4+$n/4**--$i%4];